The Chicago White Sox have pushed John Danks near the top of their offseason priorities.

According to a source, the team is trying to work a multiyear contract for the left-handed starter into their budget. So while negotiating with free agent Paul Konerko lies ahead, as well as deciding whether or not to bring back A.J. Pierzynski, not to mention retooling the bullpen, it will all be done with an eye toward Danks.

The 24-year-old still has two more years of arbitration-eligible status, but the desire is to lock him in at least through his first free-agent year in 2013. That would require a minimum three-year deal, but a four-year pact is more desirable, according to the source.

Padilla speculates that something in the $20 million range might be enough for a 4 year contract. Aaron Gleeman thinks a 4 year deal would require something around $30 million.

Padilla also says the Sox are discussing to keep their young core of John Danks, Alexei Ramirez, Gordon Beckham together. Other young players who could join that core are Sergio Santos, Dayan Viciedo, and Chris Sale.

A chance still exists for A.J. Pierzynski to be working with White Sox pitchers at Camelback Ranch just after Valentine’s Day, returning to this familiar place for a seventh season as the franchise’s starting backstop. But any sort of new deal definitely will not be arrived at before the exclusive five-day negotiating period between both sides following the World Series expires on Saturday.

“We both agreed to let things play out and take it from there,” Pierzynski told MLB.com from his Florida home on Thursday. “We both agreed to talk again, and I’m sure we will. “The door has not been shut by me or by them. There are no hard feelings from me toward them, and I hope there’s none from them toward me. Something still could be done, but if not, hopefully there’s another team who will want me.” …

1. Chris Sale / SP/RP / Sale is a tenacious competitor who belongs in the rotation long term. He displays great movement and strong command of an impressive three-pitch mix. He is far and away Chicago’s best prospect.

The rest at the link. It also lists the Top 10 White Sox players under the age of 26.